Showing papers on "Gravitational field published in 1973"

Nonuniqueness of canonical field quantization in Riemannian space-time.

Abstract: We point out and discuss an ambiguity which arises in the quantum theory of fields when the background metric is not explicitly Minkowskian-in other words, when an external gravitational field, real or apparent, is present. A general theory of a canonical neutral scalar field in a static universe, including the construction of a Fock space, is presented. It is applied to a portion of two-dimensional flat space-time equipped with a non-Cartesian space-time coordinate system with respect to which the metric is nonetheless static. The resulting particle interpretation of the field is shown to be different from the standard one in special-relativistic free-field theory. The ambiguity frustrates an attempt to define uniquely the energy-momentum tensor by the usual method of normal ordering. We discuss various suggestions for (1) distinguishing a unique correct quantization in a given physical situation, or (2) reinterpreting seemingly inequivalent theories as physically equivalent. In passing it is shown that the vacuum state and the energy density of a free field in a box with periodic boundary conditions differ from those associated with a region of the same size in infinite space; this result should be of interest outside the gravitational context.

Quasi-periodic orbits about the translunar libration point.

Abstract: Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincare and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32,379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a 'halo orbit' of the moon.

Gravitational-wave observations as a tool for testing relativistic gravity

Abstract: Gravitational-wave observations can be powerful tools in the testing of relativistic theories of gravity---perhaps the only tools for distinguishing between certain extant theories in the foreseeable future. In this paper we examine gravitational radiation in the far field using a formalism that encompasses all "metric theories of gravity." There are six possible modes of polarization, which can be completely resolved by feasible experiments. We set forth a theoretical framework for classification of waves and theories, based on the Lorentz transformation properties of the six modes. We also show in detail how the six modes may be experimentally identified and to what extent such information limits the "correct" theory of gravity.

Quantized matter fields and the avoidance of singularities in general relativity

Abstract: We consider a classical gravitational field minimally coupled to a quantized neutral scalar field possessing mass. We are especially concerned with the effects of particle creation and quantum coherence on the premises and conclusions of the singularity theorems, which imply the inevitability of singularities in classical general relativity. A closed Robertson-Walker geometry is used throughout. Nongravitational interactions are not considered. The source of the gravitational field in the Einstein equations is the expectation value of the energy-momentum tensor of the quantized scalar field. Lacking a general prescription for obtaining a finite operator from the divergent formal expression for the energy-momentum tensor, we confine our attention to situations in which plausible special methods are available. We show that quantum coherence effects in this semiclassical model can result in a violation of the energy conditions which enter into the singularity theorems. Then we exhibit numerical solutions of the coupled Einstein and scalar field equations in which a Friedmann-like collapse is stopped and converted to a Friedmann-like expansion. (In this calculation one mode of the quantum field was assumed dominant.) We conclude that quantum effects of the type considered here can sometimes lead to avoidance of the cosmological singularity, at least on the time scale of one Friedmann expansion.

New Series of Exact Solutions for Gravitational Fields of Spinning Masses

Abstract: New series of solutions for space-times which are regarded as representing the gravi­ tationaL fields of spinning bound masses is derived from a series of Weyl metrics, following Ernst's formulation on axi-symmetric stationary fields. This series of solutions includes the Kerr metric as a member of the simplest one. Except in the case of the Kerr metric, the space-times have ring singularities outside event horizons, that is, there exist naked singu­ larities. Therefore, these solutions seem to give a very different picture concerning the ulti­ mate fate of 'gravitational collapse compared with a current picture such as the Israel-Carter conjecture. , The naked ring singularity may become an active energy source of gravitational wave, and yield many interesting phenomena in astrophysics.

Gravity analysis using an exponential density-depth function; San Jacinto Graben, California

Abstract: In the analysis of gravity data over thick sedimentary basins, density contrast can sometimes be approximated by a continuous function decreasing exponentially with depth. Typical values of the exponential decrement are in the order of 0.3 to 1.5 km (super -1) . The gravity effect of an infinite (Bouguer) slab in this system tends to a finite limit as the slab becomes infinitely thick, leading to quantitative, and sometimes stringent, limitations on the resolving power of gravity analysis over deep structures. The exponential density term acts as an integrating factor in deriving the gravity effect of a prismatic building element, leading to a simple expression involving both the gravity field and its vertical derivative. A recursive computer algorithm giving the inverse solution automatically in terms of assigned density parameters is applied to a gravity profile over a graben structure at San Jacinto, California. The computed basin configuration is consistent with the seismically determined basement depth of 2.4 km and the estimated density layering of the graben fill.

Plane symmetric self-gravitating fluids with pressure equal to energy density

Abstract: Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure,p, equal to energy density,w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid withp=w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.

Nonlinear Gaseous Density Waves and Galactic Shocks

Abstract: The perturbations in the flow of interstellar gas which result from steady forcing by spiral gravitational fields of various strengths are followed. The density response is quite nonlinear even if the amplitude of the spiral field maintained by the disk stars is only a small fraction of the basic axisymmetric field. An analytical study of the properties of slightly nonlinear flows yields certain results which are qualitatively similar to those found numerically for fully nonlinear flows, Galactic shocks arise naturally, indeed necessarily, if the strength of the underlying spiral gravitational field exceeds a certain critical value. The breadth of the zone of high gas compression depends critically on whether the Doppler-shifted phase-velocity of the stellar density wave is greater than or less than the effective acoustic speed'' of the gas. In the former case, very narrow compression zones result; in the latter, quite broad zones. This distinction may explain why some galaxies have narrow optical arms while others have broad optical arms. In addition, a certain range of values for the intrinsic frequency of the wave gives rise to ultraharmonic resonances which can introduce secondary compressions of the interstellar gas. Finally, this result may relate directly to the origin ofmore » the Carina spiral feature in the Galaxy as well as to the phenomena of branches, spurs, and feathers which are often seen in external spiral galaxies.« less

Separability of the Neutrino Equations in a Kerr Background

Abstract: The first-order neutrino equations are shown to be separable in the Kerr-metric background. These equations are then used to show that the neutrino field is not superradiant, in contrast to the scalar, electromagnetic, and gravitational fields.

The wave resistance of ships

Abstract: Publisher Summary Waves follow a moving ship and the propagation of these waves is associated with the presence of a gravitational field. Water is endowed with viscosity, and anybody moving through a viscous fluid, experiences a resistance, partly because of tangentially acting stresses on the body, but partly also because boundary-layer growth, and separation, if it occurs, yield a resistance resulting from integrating normal components of the stress over the body. The frictional resistance will certainly depend upon the wave profile along the ship. On the other hand, the wave pattern itself is going to depend in some fashion upon the ship's boundary layer and wake. The effects of gravity and viscosity interact in essential ways. There seems to be no neat practicable definition of gravitational or wave resistance without introducing assumptions or approximations.

On convection and gravitational layering in Jupiter and in stars of low mass.

Abstract: Neutral helium is probably insoluble in metallic hydrogen below some critical temperature. When Jupiter has cooled sufficiently, helium droplets can form, grow, and fall under gravity, leading to chemical separation and gravitational layering in spite of rapid convection. Applications to cool stars are discussed.

Restricted Proof that the Weak Equivalence Principle Implies the Einstein Equivalence Principle

Abstract: Schiff has conjectured that the weak equivalence principle (WEP) implies the Einstein equivalence principle (EEP). A proof is presented of Schiff's conjecture, restricted to: (1) test bodies made of electromagnetically interacting point particles, that fall from rest in a static, spherically symmetric gravitational field; (2) theories of gravity within a certain broad class - a class that includes almost all complete relativistic theories that have been found in the literature, but with each theory truncated to contain only point particles plus electromagnetic and gravitational fields. The proof shows that every nonmentric theory in the class (every theory that violates EEP) must violate WEP. A formula is derived for the magnitude of the violation. It is shown that WEP is a powerful theoretical and experimental tool for constraining the manner in which gravity couples to electromagnetism in gravitation theories.

Gravity and Magnetic Investigations in the Guiana Basin, Western Equatorial Atlantic

Abstract: A free-air gravity map of the Guiana Basin between 15° N. and 6° S. in the western equatorial Atlantic, using all available shipboard and pendulum data, is presented. The gravity field is interpreted in terms of short wave-length components directly related to topographic features and a long wave-length regional field which is independent of surface or basement relief. The regional field is negative throughout the survey area, varying from −15 to −40 mgal. The magnetic anomalies over the large equatorial fracture zones indicate that the fracture zone trough is an area of zero or greatly reduced magnetization within a zone in which the magnetization is induced rather than remanent. Only about half of the gravity anomaly over the fracture zone can be assigned to topographic relief implying the presence of excess mass under the fracture zones. The gravity and magnetic evidence together suggest that large fracture zones serve as the site of intrusion of ultrabasic rocks from depth. The deformation of the lithosphere due to the sediment load of the Amazon cone and the resulting gravity anomalies were computed for various flexural rigidities, using two-dimensional elastic beam theory. The value giving the best fit to the observed gravity anomalies in both wave length and amplitude is 2 × 1023 Newton meters (nt m) (2 × 1030 dyne cm). This implies an effective lithospheric thickness of 30 km. It is suggested that the lithosphere behaves somewhat as a Kelvin (viscoelastic solid) material in its response to imposed long-term loads, approaching a minimum apparent flexural rigidity of 2 × 1030 dyne cm asymptotically in a period of a few million years.

The gravitational field of three- dimensional galaxies

Abstract: The simplest method of calculating gravitational fields is to use a set of biorthogonal pairs of mass-potential functions. A suitable set of functions for three dimensional mass distributions is derived which uses ultraspherical polynomials. Algorithms for computing the gravitational field are discussed which attempt to maximise computational efficiency.

The symmetries of Kerr black holes

Abstract: The Kerr solution describes, in Einstein's theory, the gravitational field of a rotating black hole. The axial symmetry and stationarity of the solution are shown here to arise in a simple way from properties of the curvature tensor.

Rotation of solid bodies in the solar system

Abstract: The effects of elastic distortion, nonprincipal axis rotation, precessing orbits, and internal dissipation on the rotation of a solid solar system body, which is in the gravitational field of an exterior body, are relatively easily analyzed by a Hamiltonian theory developed here. Examples of applications include the Chandler wobble, wobble of the moon, spin-orbit coupling, generalized Cassini laws, and tidal evolution.

Post-Newtonian Gravitational Effects in Lunar Laser Ranging

Abstract: The dominant-range perturbations of the lunar orbit are calculated in relativistic gravitational theory, the results being applicable to all metric theories of gravity (a class of theories which includes general relativity) By searching for the various effects calculated in this paper using lunar laser ranging, the several parametrized post-Newtonian coefficients of the metrical gravitational field can be determined, thus pointing toward specific relativistic, post-Newtonian theories of gravity and empirically ruling out other theories

New two-metric theory of gravity with prior geometry

Abstract: A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Gravitationally induced electromagnetic radiation

Abstract: A fully relativistic treatment is given to analyze the electromagnetic radiation induced by gravitational perturbations in extreme relativistic regions. For the sake of clarity, results are presented here for the simplest possible example: an uncharged mass $m$ falling radially into a field of a Reissner-Nordstr\o{}m solution. Explicit results governing the energetics of the process are found. The amount of electromagnetic radiation radiated can be of the order of magnitude of the gravitational one.

A gravitational « Aharonov-Bohm » effect

Abstract: The massless Dirac equation is considered in the presence of weak external gravitational fields. In the presence of fields arising from moving mass currents, solutions are found which are analogous to those giving rise to the Aharonov-Bohm effect in electromagnetic theory. The mass currents play the role of the magnetic fields. Comparison is made with earlier analogous solutions by Plebanski and by Balazs and Bertotti, and an alternative physical interpretation is offered in which simply connected currents can produce an effect which is observable in principle.

Geodesic synchrotron radiation

Abstract: This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.

General theory of optimal trajectory for rocket flight in a resisting medium

Abstract: This paper considers the problem of optimizing the flight trajectory of a rocket vehicle moving in a resisting medium and in a general gravitational force field General control laws for the lift, the bank angle, and the thrusting program are obtained in terms of the primer vector, the adjoint vector associated to the velocity vector Additional relations for the case of variable thrusting and integrals of motion for flight at maximum lift-to-drag ratio and flight in a constant gravitational field are obtained

Collapse of a null fluid

Abstract: An exact cylindrically symmetric solution of Einstein's gravitational field equations is given for a null fluid imploding radially along an infinite axis. This solution plays an important role in the late stages of collapse of a long cylinder of matter. One might expect that self-gravitational effects due to the increasingly relativistic mass of the collapsing matter would create arbitrarily large gravitational fields. It is shown, however, that in the null-fluid approximation the metric is everywhere regular.

A model for peaking of galactic gravitational radiation

Abstract: Geometrical optics is used to calculate the radiation pattern from a source in orbit in a strong gravitational field. No specific mechanism is postulated for the radiation itself, and only the field's effect on the radiation enters. (The model proposes a ``black hole'' at the galactic center.) Besides the Doppler peaking expected in these orbits, we find that the gravitational lens effect can enhance the radiation (regardless of how the radiation is produced). If the radiation arises from individual short events, the gravitational lensing leads to a scatter in the observed intensity. Formulas are presented for the probability a certain pulse will exceed the average by a given factor for a detector of finite sensitivity. Enhancement as found here, if present in the galaxy, would lower the overall galactic mass loss implied by Weber's gravitational radiation measurements.